Modeling How Consumers Simplify the Purchase Process by Copying Others

A Flower That Fits the Bill

Marketing borrows the biological notion of coevolution to explain the progressive “fit” between products and consumers. While evolutionary time may seem a bit slow for product innovation and adoption, the same metaphor can be found in models of assimilation and accommodation from cultural and cognitive psychology.

The digital camera was introduced as an alternative to film, but soon redefined how pictures are taken, stored and shared. The selfie stick is but the latest step in this process by which product usage and product features coevolve over time with previous cycles enabling the next in the chain. Is it the smartphone or the lack of fun that’s killing the camera?

The diffusion of innovation unfolds in the marketplace as a social movement with the behavior of early adopters copied by the more cautious. For example, “cutting the cord” can be a lifestyle change involving both social isolation from conversations among those watching live sporting events and a commitment to learning how to retrieve television-like content from the Internet. The Diary of a Cord-Cutter in 2015 offers a funny and informative qualitative account. Still, one needs the timestamp because cord-cutting is an evolving product category. The market will become larger and more diverse with more heterogeneous customers (assimilation) and greater differentiation of product offerings (accommodation).

So, we should be able to agree that product markets are the outcome of dynamic processes involving both producers and customers (see Sociocognitive Dynamics in a Product Market for a comprehensive overview). User-centered product design takes an additional step and creates fictional customers or personas in order to find the perfect match. Shoppers do something similar when they anticipate how they will use the product they are considering. User types can be real (an actual person) or imagined (a persona). If this analysis is correct, then both customers and producers should be looking at the same data: the cable TV customer to decide if they should become cord-cutters and the cable TV provider to identify potential defectors.

Identifying the Likely Cord-Cutter

We can ask about your subscriptions: cable TV, internet connection, Netflix, Hulu, Amazon Prime, Sling, and so on). It is a long list, and we might get some frequency of usage data at the same time. This may be all that we need, especially if we probe for the details (e.g., cable TV usage would include live sports, on-demand movies, kid’s shows, HBO or other channel subscriptions, and continue until just before respondents become likely to terminate on-line surveys). Concurrently, it might be helpful to know something about your hardware, such as TVs, DVDs, DVRs, media streamers and other stuff.

A form of reverse engineering guides our data collection. Qualitative research and personal experience gives us some idea of the usage types likely to populate our customer base. Cable TV offers a menu of bundled and ala carte hardware and channels. Only some of the alternatives are mutually exclusive; otherwise, you are free to create your own assortment. Internet availability only increases the number of options, which you can watch on a television, a computer, a tablet or a phone. Plus, there are always free broadcast TV captured with an antenna and DVDs that you rent or buy. We ought not to forget DVRs and media streamers (e.g., Roku, Apple TV, Chromecast, and Amazon Fire Stick). Obviously, there is no reason to stop with usage so why not extend the scale to include awareness and familiarity? You might not be a cord-cutter, though you may be on your way if you know all about Sling TV.

Traditional segmentation will not be able to represent this degree of complexity.

Each consumer defines their own personal choices by arranging options in a continually changing pattern that does not depend on existing bundles offered by providers. Consequently, whatever statistical model is chosen must be open to the possibility that every non-contradictory arrangement is possible. Yet, every combination will not survive for some will be dominated by others and never achieve a sustainable audience.

We could display this attraction between consumers and offerings as a bipartite graph (Figure 2.9 from Barabasi’s Network Science).


Consumers are listed in U, and a line is drawn to the offerings in V that they might wish to purchase (shown in the center panel). It is this linkage between U and V that produces the consumer and product networks in the two side panels. The A-B and B-C-D cliques of offerings in Projection V would be disjoint without customer U_5. Moreover, the 1-2-3 and 4-5-6-7 consumer clusters are connected by the presence of offering B in V. Removing B or #5 cuts the graph into independent parts.

Actual markets contain many more consumers in U, and the number of choices in V can be extensive. Consumer heterogeneity creates complexities for the marketer trying to discover structure in Projection U. Besides, the task is not any easier for an individual consumer who must select the best from a seemingly overwhelming number of alternatives in Projection V. Luckily, one trick frees the consumer from having to learn all the options that are available and being forced to make all the difficult tradeoffs – simply do as others do (as in observational learning). The other can be someone you know or read about as in the above Diary of a Cord-Cutter in 2015. There is no need for a taxonomy of offerings or a complete classification of user types.

In fact, it has become popular to believe that social diffusion or contagion models describe the actual adoption process (e.g., The Tipping Point). Regardless, over time, the U’s and V’s in the bipartite interactions of customers and offerings come to organize each other through mutual influence. Specifically, potential customers learn about the cord-cutting persona through the social and professional media and at the same time come to group together those offerings that the cord-cutter might purchase. Offerings are not alphabetized or catalogued as an academic exercise. There is money to be saved and entertainment to be discovered. Sorting needs to be goal-directed and efficient. I am ready to binge-watch, and I am looking for a recommendation.

“I’ll Have What She’s Having“

It has taken some time to outline how consumers are able to simplify complex purchase process by modeling the behavior of others. It is such a common experience, although rational decision theory continues to control our statistical modeling of choice. As you are escorted to your restaurant table, you cannot help but notice a delicious meal being served next to where you are seated. You refuse a menu and simply ask for the same dish. “I’ll Have What She’s Having” works as a decision strategy only when I can identify the “she” and the “what” simultaneously.

If we intend to analyze that data we have just talked about collecting, we will need a statistical model. Happily, the R Project for Statistical Computing implements at least two approaches for such joint identification: a latent clustering of a bipartite network in the latentnet package and a nonnegative matrix factorization in the NMF package. The Davis data from the latentnet R package will serve as our illustration. The R code for all the analyses that will be reported can be found at the end of this post.

Stephen Borgatti is a good place to begin with his two-mode social network analysis of the Davis data. The rows are 18 women, the columns are 14 events, and the cells are zero or one depending on whether or not each woman attended each event. The nature of the events has not been specified, but since I am in marketing, I prefer to think of the events as if they were movies seen or concerts attended (i.e., events requiring the purchase of tickets). You will find a latentnet tutorial covering the analysis of this same data as a bipartite network (section 6.3). Finally, a paper by Michael Brusco called “Analysis of two-mode network data using nonnegative matrix factorization” provides a detailed treatment of the NMF approach.

We will start with the plot from the latentnet R package. The names are the women in the rows and the numbered E’s are the events in the columns. The events appear to be separated into two groups of E1 to E6 toward the top and E9 to E14 toward the bottom. E7 and E8 seem to occupy a middle position. The names are also divided into an upper and lower grouping with Ruth and Pearl falling between the two clusters. Does this plot not look similar to the earlier bipartite graph from Barabasi? That is, the linkages between the women and the events organize both into two corresponding clusters tied together by at least two women and two events.

The heatmaps from the NMF reveal the same pattern for the events and the women. You should recall that NMF seeks a lower dimensional representation that will reproduce the original data table with 0s and 1s. In this case, two basis components were extracted. The mixture coefficients for the events vary from 0 to 1 with a darker red indicating a higher contribution for that basis component. The first six events (E1-E6) form the first basis component with the second basis component containing the last six events (E9-E14). As before, E7 and E8 share a more even mixture of the two basis components. Again, the most of the women load on one basis component or the other with Ruth and Pearl traveling freely between both components. As you can easily verify, the names form the same clusters in both plots.


It would help to know something about the events and the women. If E1 through E6 were all of a certain type (e.g., symphony concerts), then we could easily name the first component. Similarly, if all of the women in red at bottom of our basis heatmap played the piano, our results would have at least face validity. A more detailed description of this naming process can be found in a previous example called “What Can We Learn from the Apps on Your Smartphone?“. Those wishing to learn more might want to review the link listed at the end of that post in a note.

Which events should a newcomer attend? If Helen, Nora, Sylvia and Katherine are her friends, the answer is the second cluster of E9-E14. The collaborative filtering of recommender systems enables a novice to decide quickly and easily without a rational appraisal of the feature tradeoffs. Of course, a tradeoff analysis will work as well for we have a joint scaling of products and users. If the event is a concert with a performer you love, then base your decision on a dominating feature. When in tradeoff doubt, go along with your friends.

Finally, brand management can profit from this perspective. Personas work as a design strategy when user types are differentiated by their preference structures and a single individual can represent each group. Although user-centered designers reject segmentations that are based on demographics, attitudes, or benefit statements, a NMF can get very specific and include as many columns as needed (e.g., thousands of movie and even more music recordings). Furthermore, sparsity is not a problem and most of the rows can be empty.

There is no reason why each of the basis components in the above heatmaps could not be summarized by one person and/or one event. However, NMF forms building blocks by jointly clustering many rows and columns. Every potential customer and every possible product configuration are additive compositions built from these blocks. Would not design thinking be better served with several exemplars of each user type rather than trying to generalize from a single individual? Plus, we have the linked columns telling us what attracts each user type in the desired detail provided by the data we collected.


R Code to Produce Plots

library(latentnet)
data(davis)
davis.fit<-ergmm(davis~bilinear(d=2)+rsociality)
plot(davis.fit,pie=TRUE,rand.eff="sociality",labels=TRUE)
 
library(NMF)
data_matrix<-as.matrix.network(davis)
fit<-nmf(data_matrix, 2, "lee", nrun=20)
par(mfrow = c(1, 2))
basismap(fit)
coefmap(fit)